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How does elevator control effectiveness change with altitude/ air density?
Suppose an unpowered, rigid, mechanical, lightweight aircraft (e.g. sport glider) is descending at a steady glide in a constant trim (hands off) configuration in a standard atmosphere. The pilot applies a quick elevator input and then goes hands off again, causing the nose to pitch up and the glider to gain altitude momentarily before eventually returning to a steady glide.
Suppose we measure the maximum angle of attack reached, (or max pitch angle, if that's easier), the maximum altitude gain, and the time it took to reach those maximums after the control input.
How would those values (max altitude gain, max angle, and times to get there) differ if the same control input occurred at 5,000 feet vs 10,000 feet above sea level? Support your answer using physics/ aviation formulas or reputable references.
My thoughts so far
Since the "effective" air speed of the glider in a particular trim configuration is expected to remain the same across altitudes, then I would assume the lift and drag force changes generated by the control input would be the same at any altitude.
However, the "true" airspeed of the glider is from what I could find about 10% higher at 10k, which results in greater momentum to resist changes in motion and greater kinetic energy that can translate into height.
However, I'm not sure if those two (momentum vs kinetic energy) would cancel each other out.
If kinetic energy alone is considered, I'd expect the altitude gain to be greater at higher altitudes, and I'm not sure about max angles or the times to get there.

Control effectiveness as in rate of change in direction will be greater in denser air.  At higher altitudes, momentum is greater as you pointed out, for the same directional change force.  Much easier to stall.  What is interesting is altitude gain after control input if it is sustained.

@RobertDiGiovanni Do you know of any proofs of "easier to stall"/ easier to change angle, or even a research paper/ controlled experimental data that verifies this for fixed wing aircraft?

My thoughts, not really very consolidated yet: inertial effects are much larger, in relation to aerodynamic effects, at high altitude.  So for the same control input (elevator moves x degrees and stays there for y seconds and then is allowed to go back to trim), the change in angle-of-attack is bigger at low altitude.  Or is it?  Because once the glider begins pitching up, there is less aerodynamic damping at high altitude, so the motion will continue for longer after the pilot releases all pressure on the stick.  ??? It's complicated.

@quietflyer Indeed it is complicated. So far my search has led me to flight dynamics textbooks, which are full of very long and complicated equations modeling this in 6-9 axes. I'm just hoping this simple aspect of it has been figured out already, in a way that doesn't require me to take a year of physics and math courses.

@Oleg very hard to stall a paper airplane as it's pitch change can keep up with change in AoA.  As you go faster at higher altitude, aerodynamic force  from elevator is the same but momentum is greater.  The plane rotates at the same rate but pitches (changes direction) slower.

What you describe is called a doublet. You fly at a trimmed state, then move the stick momentarily to a different position and back to the original position again. Then you watch what happens.
Traditionally, differential equations were used to describe the results and I guess that is what you still find in flight dynamics textbooks. There, the second derivative term describes inertial effects and the first derivative term describes damping effects. So far, you only looked at the inertial effects, which do indeed get bigger with the inverse of air density.
However, damping is at least as important, and this term also is affected by air density: Damping goes down with the square root of density. Not only will the excitations from a doublet grow from inertial effects, but the countering forces from stability will become weaker, so it will take longer for them to stop the resulting motion.

I'm not sure about max angles or the times to get there

Lowered damping due to a higher altitude will make the angle deviations larger and reduce the eigenfrequency of the resulting motion by the inverse of the square root of the density ratio between your reference and actual altitude. The excursions will become slower and larger by the increase in true air speed. Things will take longer to die down, so it will take more oscillations until the motion dies down.
If the trimmed state does not change with altitude, the true air speed goes up with the inverse of the square root of the change in density. The speed of the pitch response is proportional to the frequency of the short period mode which again depends on the stability margin, pitch damping and density as explained in the linked answer.

Thank you, you seem to know a lot about the topic. Is there any chance you can go into more detail, mathematically, about that INITIAL pitch change? By what percent will the angle/altitude differ between 5k and 10k? By what percent faster will they occur? How much of that is due to inertial vs dampening effects? Are there simpler equations I could use to calculate this myself or with a math-only tutor?

I looked into flight dynamics with the help of some tutors. I understand now that the math is too complicated for a "simple" answer to my post.

You mentioned "traditionally". What is the modern alternative? Computer simulation?

@Oleg Of course. Specifically, the finite difference method. For the equation of the time dependency of the pitch response see the newly linked answer, which contains an approximation for the short period mode frequency.


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Does ground effect affect a paraglider/ canopy?
I've heard that ground effect is only significant if the wing is closer to the ground than its span, and I've never seen a canopy/ paraglider that would qualify for that.
Is that true or would there be some significant effect? (Based on theory or at least data.)
Let's assume that there is no bank/ roll (which is a separate question).
My thinking is that even if the ground effect does not reach the wing but somehow affects the pilot's body or the lines, it might just be enough to be significant.
This is because parafoils are lighter, softer, and with greater CL-CG moment than most aircraft, so minor effects (such as drag bowing the lines, drag on the pilot, or the mass of the air being pulled along outside the wing) can significantly change the trim or performance.

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Can partial flow separation make the effects of Reynolds number on stall more significant?
While discussing this stall differences with altitude question with a skydiving canopy designer, I told him that most people seemed to think Reynolds would not be significant at these altitudes.
His thought was that it might be different in a canopy, because

Airflow is separated even before stall on a big portion of the canopy. It's specific to [the] way toggle[s] distort the trailing edge.

So...
Can partial flow separation make the effects of Reynolds number on stall more significant?
My thoughts:
I read that lower Reynolds number reduces the stall angle of attack due to increased skin friction. I can't think of how friction would scale differently due to flow separation.
Perhaps Reynolds number could affect the turbulent flow of the separated area?
Or could it simply take less to "tip the stall over the edge" to where it's noticeable?

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OBI, RMI, HSI... What combination do GA aircraft w/o glass typically have?
I'm learning about radionavigation, and all the various analog displays that can be used:

Automatic Direction Finder (ADF) - Provides basic bearing information to practically any radio source the pilot can tune to. Designed for use with the older NDB system developed during WWII, still in use but about two generations redundant in the face of VOR and GPS. Later models include a manual compass card to reduce mental math.
Radio-Magnetic Indicator (RMI) - A two-channel ADF with compass card slaved to the magnetic compass (or in some cases using an internal gyro like the Heading Indicator).
Omni Bearing Indicator (OBI) - Used for VOR navigation and the cheapest way to do so, has a manual compass card that selects the desired VOR radial and a CDI needle to provide a steering aid to place the aircraft on that radial, with a "TO/FROM" indicator to resolve directional ambiguity.
Horizontal Situation Indicator (HSI) - Combines the OBI with the aircraft's gyroscopic direction indicator to provide a simplified "moving map", with the aircraft's current heading, relative direction of the selected VOR radial, course deviation and glide slope all in one instrument. Can replace the Heading Indicator as well as an OBI to reduce instrument count and/or allow for redundant backups like a second artificial horizon. Biggest downside is cost (about $13k for the display unit itself).
Distance Measuring Equipment (DME) - essentially IFF in reverse; the aircraft interrogates a ground station with radio pulse pairs, and the station sends a matching pulse pair after a specially-timed delay; total round-trip time of the interrogation and response, minus the preprogrammed delay and halved, is the time the signal took to reach the station at the speed of light through air (about one nmi in 12.36 microseconds), which can then be used to calculate distance. These transponders are often colocated with NDB or VOR stations on a corresponding frequency allowing aircraft to get an accurate fix from a single ground station.

My understanding is that, for an aircraft to be suitable for IFR flight, the aircraft requires all VFR instruments (airspeed, altitude, compass, tach, oil pressure, oil or coolant temp, fuel gauge) plus a timepiece, gyroscopic direction indicator, Turn Coordinator or Turn/Slip Indicator, adjustable pressure altimeter, artificial horizon, and "two-way radio communication and navigation equipment suitable for the route to be flown", that last requirement being just wonderfully ambiguous regarding what you as a pilot may want or need from the above listed equipment.
The standard configuration for the 172 and Cherokee seems to be two OBIs, one with glide slope and one without, plus a single-channel ADF. This seems like a fairly economical gauge cluster for modern radionavigation, but the ADF seems old-fashioned in the face of the newer RMI that allows triangulation from an ADF and a VOR or two VORs more or less at a glance.
Obviously the very newest and most expensive aircraft have full glass cockpits, but for the rest of us, what displays are typically used? Do people tend to upgrade the ADI to an RMI, or is that the display that's considered redundant with NDBs on their way to retirement? How many people spring for the HSI? Do you keep the non-GS OBI if you have an HSI, or do you replace that with something else too? Is DME standard equipment, can't fly without it, or do pilots more often rely on multi-station triangulation for a position fix?

First, I think this is a good question that should be kept.  That said, it sure does split into a whole lot of little questions at the end there.

This is an excellent resource question for those of us who are non-pilots. It helps explain in one simple step what many of the acronyms are. If you'd spell out HSI and DME it would be ideal (for the ones you've included).

@SteveV. I admit there are a few additional questions but they're all really clarifiers to the main question, specifying the type of information I'm after.

"two-way radio communication and navigation equipment suitable for the route to be flown", that last requirement being just wonderfully ambiguous regarding what you as a pilot may want or need …

That statement isn't ambiguous at all. You can file and fly IFR with a transponder and a VHF comm radio if you can get controllers to issue you radar vectors for the route -- just be making a visual approach at your destination (or something like an ASR or PAR approach where you get your guidance from a controller).
Of course since your question was not "How do I piss off ATC?" that's neither here nor there - you're asking about typical instrument configurations in GA aircraft (for purposes of this answer I'm going to assume you mean the usual "Light GA / trainer" sort of aircraft - typical Pipers, Cessnas, Beechcraft, Mooneys, etc.)
It's hard to nail down "typical" because it's a rapidly moving target these days. When I started flight training two Nav/Com radios and an ADF was a pretty sweet IFR airplane, even if the ADF was a little sketchy. Now even a six-pack cockpit has a good chunk of glass in the panel in the form of a GPS (Garmin 430 or similar), and people are ripping out ADFs as the FAA decommissions them, but I poked around at some of the rental fleets near me  and it seems to shake out like this as of right now:

Most IFR aircraft have dual OBIs. If there's a GPS they tend to both have glideslope capability (either connected to two GPS Nav/Coms or one to the GPS and one to a traditional Nav/Com radio that has a glideslope receiver).

Older planes with dual Nav/Comm radios often have glideslope capability on the #1 Nav/Com & not the #2 radio, which is why you often see one OBI with a glideslope needle and one without.

Older IFR trainers tend to have ADFs still. Some are placarded as INOP and are basically heavy, drag-producing AM Radios (the Mets won).

Aircraft with a GPS rarely have an ADF, because the GPS can usually display the ADF indications using a "normal" OBI. One less thing for the pilot to have to remember how to operate.

I've never seen a light GA aircraft with an RMI.
They're probably out there but I doubt they're common. Slaving them to the magnetic compass requires equipment which is not cheap, and as ADFs are dying out there's not much benefit to installing one now.
None have HSIs, but I have seen a few planes around with them.
My sense here is it tends to be an owner-installed upgrade because the pilot wants it and they have the money to spend on it. Like you noted they're still pretty expensive, mainly because they're rather complicated bits of equipment combining a vacuum-powered DG, a bunch of sensors, and a VOR/LOC/GS presentation.

Every HSI installation I've seen takes the place of the Nav 1 OBI.
What gets put into the now-vacant hole varies from aircraft to aircraft. This Cessna has an ADF card there (thanks to CFC for the photo)

Very few have DME.
If you're flying on Victor airways you're pretty much always flying toward some VOR (so you have one needle that won't move), and you can easily get a cross-bearing from a VOR that would be roughly perpendicular to your route to find your current position on the chart.
The DME gives you this in Distance/Direction form without needing to tune a second VOR or draw on your chart, and it can do nice things like give you an approximate groundspeed, but that doesn't make it indispensable.

A reason many IFR trainers lack a DME seems to be because on the IFR checkride you can't be tested on equipment that's not installed: If you have no DME you can't be asked to fly a DME arc.
DME is another technology that's being made redundant by GPS: The GPS can give you distance and bearing to any arbitrary point, and that point can easily be a VOR. It can also compute groundspeed.

An ever-increasing number have large chunks of glass somewhere in the panel.
As GPS installations become more common it's increasingly rare to find a plane without a moving map display next to the six pack. The GPS provides the magic "Magenta Line" and also typically feeds an OBI (or HSI).
If the OBI or HSI fails the GPS can usually also display a digital OBI on its display.

Excellent answer, very informative. Re: the ADF, I didn't realize it was a separate radio from the Comm/Nav unit. I thought you tuned NAV 1/2 to the ADF station and it pointed the way. As far as usefulness, if it'll pick up and direction-find commercial AM radio, then if you know where the transmitting tower is it could have some remaining NAV use once the NDBs are gone, albeit at shorter range.

@KeithS Yeah the ADF is a separate box in every installation I've ever seen - the underlying radio principles are fundamentally different from a VOR, as is the frequency range, so it doesn't make much sense to combine them. An ADF will find AM radio towers quite well, but unfortunately those tend to move around a little as station owners look for cheaper leases for their gear (though they seem to be less volatile than FM transmitter locations).

Many higher performance singles have HSIs and DME bc they are often used for long XC IFR.

@rbp Yeah, if you step up to the Cessna 210 & such you've probably got a better change of finding a DME (unless it's been replaced by a GPS). I haven't seen many HSIs though (the only plane on the ramp by me that I know has one is a CAP 182) - we're talking mostly owner-flown older aircraft (1960s-1980s) though, HSIs may be more common in newer (1990s/2000s) stuff, especially if it was a factory option.

If you mark the ADF as INOP, the DPE can't make you do an NDB approach on a checkride; I suspect many of them actually work just fine.  Actually taking it out would save some weight but costs real money.  The few HSIs I've seen in rental trainers replaced the DG, and the second OBI (usually the one without GS) was also removed.

@voretaq7 Cessna 210's have a HSI as standard equipment.

GPS equipped planes, especially with newer GPS/NAV/COM Flight Management Systems (FMS), may have an older NAV/COM radio with CDI for ILS/LOC/VOR approaches, and then a DG/HSI connected to the FMS. Avidyne IFD540 & Garmin G5 DG/HSI would be one combination, with autopilot as well.

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What are all the ways that wind velocity can affect a paraglider/ canopy before it touches the ground?
Let's assume that a "perfect" humanoid robot flying a ram air parafoil (paraglider or canopy) performs some maneuver for landing exactly the same way multiple times.
The only difference between the trials is the wind velocity relative to the ground (downwind/ crosswind/ upwind/ no wind/ etc...).
We collect statistics for a bunch of sensors (airspeed, vertical speed, etc...) for each trial until just before contact with the ground.
Question: What are all the things that we know (via theory or repeatable experiments) that would cause detectable difference in the statistics due to the wind velocity OTHER than ground speed or direct interaction with the ground?
What I've already come up with
(Feel free to correct me on any of these)

A wind shadow or wind gradient would cause the canopy to pitch forward and lose some effective airspeed / lift/ (energy?) momentarily while flying upwind. The opposite would happen flying downwind.

I've heard that gusts are sharper on the upwind side due to how pressure waves work. In this case, the "average" effect of each gust would be the same whether you are flying upwind or downwind, but you might detect a difference in the average shape of oscillations if you always fly through the sharp side first (upwind) or the gradual side (downwind).

And here is one I'm still thinking through:

I've heard that ground effect only applies if the wing is closer to the ground than the span, and I've never seen a canopy/ paraglider that would qualify for that. (Is that true or would there be SOME detectable effect?) However, pilots can bank a canopy during landing, lowering a wing tip right to the ground. Would this enter ground effect? If so, I'm assuming a crosswind would interact with this somehow?

Assumptions:

Let's assume an infinite number of trials, so random events that don't follow a pattern (such as individual thermals or gusts) can be ignored. However, things that follow patterns (such as wind gradient generally decreasing towards the ground) should be considered.

Let's assume a flat, circular landing field that is longer/ wider than the maneuver requires. It is symmetrical in all directions. It may or may not have buildings and trees surrounding it (also symmetrical).

Let's assume the parafoil has stabilized in whatever air mass it's in before starting the maneuver.

The maneuver might be anything from multiple 360 turns to build speed for a freestyle CP competition, to a simple flare from half brakes. Anything that a human might regularly perform.

The canopy might be anything from a lightly loaded large paraglider to a heavily loaded, high performance competition canopy. Anything that an average size human might regularly fly.

A note about parafoils:
Parafoils are much lighter and have much greater separation between CG and CL/ CD than any other aircraft. They have a uniquely soft, flexible wing that may be full of air.
As a result, effects that are thought to be insignificant in other aircraft types can be very significant in parafoils.
Examples:

The "apparent mass" of the air being dragged along by friction.
Line drag bowing the lines, which changes the trim.
Significantly more dynamic responses to control inputs in lower air density

So I'm particularly curious if any of these relate to wind-related effects that wouldn't be a factor in other types of aircraft.

Re "I've heard that gusts are sharper on the upwind side due to how pressure waves work. In this case, the "average" effect of each gust would be the same whether you are flying upwind or downwind, but you might detect a difference in the average shape of oscillations if you always fly through the sharp side first (upwind) or the gradual side (downwind)."  -- this alone would be worthy of it's own question, or maybe two (one about the asymmetric shape of the gusts, and one about the resulting effect on flight dynamics.)

@quietflyer Thanks. I actually did expect more questions to come out of this question! Your comment confirmed that it's a thing, so I'll move it out of the uncertain category and that's good enough for this question. :) I'll create those two questions when I get a chance (unless you'd like to beat me to it).

Here’s one, based on my own experience: wind shear (or wind gradient) does appear to affect lift.  What I’ve observed when soaring a hill is that I can fly into wind for some distance (hundreds of metres) without losing any height but then I turn downwind and sink steadily until I return to the hill.  My rationalisation is that even at a few hundred feet there’s still a shear as the air speeds up to go over the hill.  My wing generates lift by having the air over the upper surface going faster than the air underneath, so when heading into wind the shear assists this and when flying downwind the shear works against the airflow differential that the wing generates.  Since this effect is apparent at altitude it’s very likely to be significant when close to the ground.  Hence when landing into wind (as is normal) you will experience something similar to ground effect.  As regards to ground effect itself (as would be experienced in still air) the effect seems to be very small but probably not immeasurable.  TL;DR landing upwind in a breeze has a lower rate of descent than in still air.

Interesting! I've never heard of this. It seems the opposite of the wind gradient effect (where landing into the wind might reduce lift, if the wind speed is decreasing towards the ground). Do you have any links or references for this wind shear effect?

I don’t have track log data with accurate height, my observations were based on a variometer which would indicate minimal change in pressure altitude while flying around 500m into wind but then lose around 200ft while flying downwind.  The sink rate was steady in straight flight and couldn’t be attributed to losses while turning.  It’s quite repeatable, most easily done in evening conditions where the wind is steady and minimal thermic activity.

Regarding wind shear near the ground, I don’t have any references other than my own experience.  Because if the nature of paragliding it’s difficult to repeat observations under identical conditions, and pilots are generally more interested in horizontal rather than vertical speed when landing, so gathering objective data would be challenging.

what about a reverse wind gradient? If I remember correctly, the wind near a rounded hill is strongest at the level of the peak. So if you were returning above the hill, you'd have been going into faster and faster wind. The effect would have reversed below the top of the hill, possibly without you noticing since by that point you'd have already returned to the ridge lift.

I couldn’t rule that out


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How does ground effect work with a banked wing?
How would an explanation of ground effect such as this one from Peter Kämpf be modified to account for a highly banked wing?
A paraglider and HP canopy pilot told me that when he banks a wing to touch a tip to the ground (as a trick) that he feels resistance and has to add control pressure to complete the maneuver. Presumably, this is due to ground effect.
I'm still wrapping my head around ground effect, and this isn't quite fitting with my mental imagery. The "cushion of air" goes away, the down wash is no longer blocked, etc....
Just a guess: maybe the ground is blocking the spanwise flow?

"I'm still wrapping my head around ground effect, and this isn't quite fitting with my mental imagery. The "cushion of air" goes away, the down wash is no longer blocked, etc....": this might help.

A short version of A.C.A.'s answer:
Peter's answer ends with "This effect disappears once the wing is far enough from the ground."  So for a bank that is steep enough and close enough to the ground, the lower wing sees more ground effect: more lift and less drag.  That's the only modification.  The lower wing sees more.
Let's apply that to your friend's observations.
"More lift" on the lower wing explains why he needs to increase (roll) control pressure, to avoid rolling out of the bank.
"Less drag" predicts that his yaw rate would reduce.  If he had a rudder (paragliders don't), he'd have to apply more of that too.  But if his "trick" is more like a pirouette than steady knife-edge flight, and his yaw control is a side effect of commanding roll, then that's yet another reason to command extra roll.

Thanks, that also helps, and maybe that's all there is to it. But consider this: at the wing tips there is spanwise flow. Wouldn't that interact differently with the ground than downwash? The pictures I've seen of tip drags have the wing almost perpendicular to the ground. E.g. https://www.fai.org/news/swoop-freestyle-international-open-saudi-arabia

A startling photo!  Such a maneuver must have a high pitch rate and other dynamic effects, which a steady-state analysis would miss.  @PeterKampf???

When an aircraft is shorter than its wingspan from the ground, the ground effect happens. Because of the ground's interference with the downwash and wingtip vortices, it increases lift and decreases the generated drag.
Relating to this concern, banking also involves causing a horizontal component of lift that enables the aircraft to change its direction by tilting the aircraft wings relative to the main part, which is the horizontal plane.
Moreover, in a situation where the plane is in a banked position, the lower wing is closer to the ground than the higher wing. At this time, the lower wing increases lift and reduces drag more than the higher wing. Following this, a rolling moment may happen. So, the aircraft might require more aileron input to keep a stable banked position due to the stronger lift on the lower wing.
Generally, pilots need to be aware of these changes, especially during low-altitude maneuvers like takeoff, landing, or low passes, since the aircraft's stability and control responses can be affected.
In conclusion, an airplane with banked wings experiences asymmetric lift and drag when it flies close to the ground because the lower wing is more affected by the ground effect than the upper wing. In order to preserve stable and organized flight, I recommend the pilots modify their control inputs due to the potential impact of this asymmetry on the rolling and turning dynamics of the aircraft.

Thank you, I learned stuff while reading this, but my question is more about how the causes (e.g. ground wash and wing tip vorteces) themselves are affected by the large bank angle.

Welcome to Aviation SE!  But please be careful that your answers really answer the question.  Don't bother to define terms (bank, ground effect) that the questioner used and already understands.


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Does partial flow separation due to toggle input affect the physics of paraglider/ canopy controls?
A skydiving canopy designer said the following:

Airflow is separated even before stall on a big portion of the canopy.... It's specific to [the] way toggle[s] distort the trailing edge.

Is this true, and if so, how would this fit into our understanding of how paraglider controls work or the equivalent for (the much less efficient) skydiving canopies?
My thoughts:

If this were true, wouldn't we see a lot of fabric deformation on parts of the wing in deep brakes? Yet the images below look smooth.

Would flow separation reduce lift without affecting drag? This might help explain why toggle inputs are much more "draggy" than ailerons.

Is this why toggles increase the chance of front collapse? (I'll make a separate question for this)

I'm guessing that this is less significant in modern paragliders, which seem to have less distortion with toggle input.


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What is the smallest manned aircraft with four engines?
What is the smallest (by operating empty mass) quad-engine aircraft that satisfies these conditions?

Current or past airplane
aircraft with fixed wings, not a rotorcraft, not a lighter than air, etc
4 engines, pistons or turbines
fuel as a main source for propulsion
actual aircraft, not scaled model
piloted by a pilot or a crew
used for an actual military or scientific goal or business (not for design tests only).

Added to prevent flying suits to be proposed:

Need to takeoff and land under its own power.
Not a worn wing (flying suit), the aircraft must have a flight deck where the pilot can be.

If this one had been piston or turbine, it would be a good candidate:

... but it's an electric-powered aircraft.

The little twin is a Cri Cri homebuilt originally from France. It is not electric. The initial design had 2 very small gas engines. There have been several builders that used very small turbines (jet) engines.

Why limit to military/scientific/business?  How about just personal use?  And how exactly do you differentiate "wear"?  Does it have to have landing gear?  That'd leave out some ultralights.  Not to mention that I've owned a few cars, most recently a Miata, which some people might think of as wearable :-)

"How about just personal use?", not excluded, but the ones you can buy. I'm trying to exclude experimental overpowered planes which could also fly with only 2 engines.

The Short Scion Senior flying boat was powered by four 88 hp radial engines and its weight, empty, was 3,650 lb (1,637 kg).

I present you Yves Rossy's Jet wingpack, which satisfies your conditions (I know I'm pushing it, but couldn't resist).

Yves Rossy's Jet wingpack, By Rama - Own work, CC BY-SA 2.0 fr, Link
It is certified by FAA as an aircraft, powered by four Jetcat P400 turbojets, piloted by an individual, not a rotorcraft and used in show business.
According to the official site, it weighs 150 kg.

@ymb1's logic is correct. To get to lightweight four engined aircraft with, you have to go back when the engines were not powerful enough for large aircraft. So, I present you the Sikorsky Ilya Muromets, the World's first four engined bomber.

Sikorsky Ilya Muromets, By www.cultinfo.ru, Public Domain, Link
The Ilya Muromets Type S-23 V is reported to have an OEW of around 3700 kg, powered by four Sunbeam Crusader engines. Its predecessor, the Sikorsky Russky Vityaz, was still lighter, though it never saw service in numbers, sadly.
Of course they are not autonomous as per your requirement. Why would you want a manned autonomous aircraft anyway?

Ok, good try and +1 for that. I've added the constrains to be autonomous, not requiring being launched from another aircraft.

@mins: It might be good to specify in your question that you mean the aircraft must launch and land without assistance from other aircraft, since the term usually refers to the ability of a vehicle to operate without assistance from a human operator.

I've always wondered why they didn't go to 4-engine craft pretty much the moment it was possible to build a wing long enough.  Especially given the reliability of early engines.

Why would you want a manned autonomous aircraft anyway? - for the same reason I want a manned autonomous car... so I can fly places without being a pilot.

It's an entirely different kind of flying, altogether!

The 1800 lb “Bally Bomber” is the smallest and lightest 4 engine, manned, conventional aircraft.
It is a 1/3 scale B-17.

Hi Mike, nice addition and certainly great engineering, however it doesn't seem to meet the criteria (scaled reproduction, not a true aircraft you can buy, not an aircraft with an actual mission).

When you said "actual aircraft, not scaled model" I thought you were talking about RC aircraft.

Can I suggest the DH Heron, which first flew in 1950. It was a development of the DH Dove, with a lengthened fuselage and 4 engines. This (according to Wikipedia) weighed in at 3700kg.
DH Heron.

If you choose DeHavilland, may I suggest an earlier type? The DH 86 Express weighted less than 2800 kg empty.

Smallest commercial jet with 4 turbines is probably the BAe 146-100.
https://en.wikipedia.org/wiki/British_Aerospace_146

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Safety factor in aircraft design
How can a plane withstand the safety factor of 2.5?

Are you asking about safety factor or load factor?

I'm asking about safety factor

Safety factor describes the structural capacity of a system beyond the expected loads or actual loads. So, safety factor gives how much the system is stronger (i.e. how much load it can take before failure) compared to the expected load on the system.
$ Safety \ Factor = \frac {Maximum \ load \ before \ failure}{Design \ load}$
Design load, sometimes called the limit load is the maximum amount of load the part is expected to face in service. In aviation, the FAR Part 25 deals with safety in §25.303   Factor of safety, which says,

Unless otherwise specified, a factor of safety of 1.5 must be applied to the prescribed limit load which are considered external loads on the structure. When a loading condition is prescribed in terms of ultimate loads, a factor of safety need not be applied unless otherwise specified.

As can be seen, the safety factor is the structural load for which the system has been designed, not a load that actually acts on the system. The main reasons for having a factor of safety are,

Loads may be high in certain unexpected situations (like emergency)
The structure may undergo wear and tear and my degrade over time.
The structure may be loaded beyond the expected loads inadvertently.

Except in unusual circumstances, the aircraft will not to withstand any safety factor; rather is is designed to withstand safety factor times the maximum expected load. The figure of 2.5 is too high for safety factor in aviation and has not been used in any aircraft to the best of my knowledge due to the exorbitant weight penalty involved.
The term used for withstanding of load is called load factor, which is given as the ratio of aerodynamic load perpendicular to longitudinal axis to the aircraft weight.


text:
What are those in the belly of a 747?
In the next picture what are the items circled in red?

Photographed by Adrian Pingstone in August 2002 and released to the public domain.

related, if not duplicate: https://aviation.stackexchange.com/q/16566/1467

This is what is on the other side. Additional details: Why is air mixed with bypass air on the A/C of an aircraft?

The forward ones are a ram air inlet (NACA duct) for the Environmental conditioning System (ECS) and what looks like an antenna. The aft one is an exit louver for the ECS.

@Federico You're right. I didn't see that :). Looks like an antenna.

I don't think it's an antenna, I think it's a drain, similar to here.

The forward inlets are air inlets for the air conditioning and pressurisation.
I am not sure of the after ringed area.


text:
What is the physical meaning of circulation found in Kutta condition?
The Kutta–Joukowski theorem is applicable for 2D lift calculation as soon as the Kutta condition is verified. When this is the case, there is a circulation $\small \Gamma$ around the airfoil. My question is related to this circulation:

What is the physical meaning of the circulation $\small \Gamma$, often represented like this (example 1, example 2, example 3):

(Own work)

I'm interested in a simple explanation of the circulation (is air moving around the airfoil? for dummies) and how does this circulation relate to a view of the airflow in a wind tunnel, where there is no apparent air flowing clockwise around the airfoil:

Source: Youtube
The rest of this post is a presentation of the circulation theory which motivates my question, and as I understand it, but is not part of the question.

The Kutta condition is linked to stagnation points, the points where air tubes separate to flow on a given side of the airfoil, and where they join again behind the airfoil. The Kutta condition stipulates the latter point coincides with the airfoil trailing edge:

Wikipedia: A body with a sharp trailing edge which is moving through a fluid will
  create about itself a circulation of sufficient strength to hold the
  rear stagnation point at the trailing edge.

(Own work)

According to theory, when the airfoil moves through air, the circulation moves the rear stagnation point to the trailing edge, and then maintains it at this position. When at this position, the circulation is finite and can be used to compute lift with Kutta–Joukowski theorem:

Wikipedia: The theorem relates the lift generated by an airfoil
  to the speed of the airfoil through the fluid, the density of the
  fluid and the circulation around the airfoil. [...] The lift per unit
  span $L^{\prime}$ of the airfoil is given by:
$$L^{\prime} = −\rho_{\infty} V_{\infty} \Gamma$$
where $\small \rho_{\infty}$ and $\small V_{\infty}$ are the fluid
  density and the fluid velocity far upstream of the airfoil, and and
  $\small \Gamma$ is the circulation defined as the line integral
$$\Gamma = \oint _{C}V \cdot d \mathbf {s}$$
around a closed contour $C$ enclosing the airfoil and followed in the
  positive (anti-clockwise) direction.

That video shows an airfoil shedding vortices, but that has little to do with the main question, that may be formulated as follows: Does a speck of dust caught in the midst of that 'circulation', really revolves round the wing...? or is the Kutta-Joukowski circulation just a useful mathematical construction...?

Circulation of a fluid around an object by itself will produce no lift. The classic example of this is the spinning cylinder with no other airflow. Viscosity will cause the fluid near a cylinder rotating clockwise to circulate in a clockwise direction around the cylinder. If a left to right horizontal flow is introduced there will be a vector sum of the two flows. This results in the stagnation points near 8 o'clock and 4 o'clock (as opposed to the cylinder with no rotation in the left to right flow having the stagnation points at 9 and 3 o'clock.) The net result of this is the Magnus effect where lift is generated in the 12 o'clock direction.
In your first diagram (typical inviscid flow) there is no circulation. The shape of the airfoil in viscid flow causes the trailing stagnation point to move to the trailing edge (second image -- the Kutta condition). This has the same effect on the airflow as the spinning of the cylinder, in that it creates a clockwise circulation about the airfoil.
The line integral describes, for an arbitrary closed contour around the object, the dot product of the fluid flow velocity vector with the vector path moving around the contour. The simplest contour to analyze is created by following flow streamlines above and below the airfoil and connecting them before and after the airfoil with lines perpendicular to the streamlines.
Since the dot product of perpendicular vectors is 0, the integral along perpendicular portions of the contour are 0. The dot product of parallel vectors  is just the multiplication of the scalar values, and since the direction of the contour is reversed between the upper and lower streamline the effect is adding one and subtracting the other. Due to differences in lengths and the different flow speeds (Bernoulli...) along the contour, the integral is non-zero. This number represents the net effective circulation about the airfoil (total flow minus the horizontal flow.)
The interesting thing is that if you extend the contour behind the airfoil far enough to enclose the wake of the airfoil from the beginning of movement, the circulation will be zero as the circulation of total wake is the vector opposite of the circulation about the airfoil.

There is no molecule in the air which actually revolves around the airfoil in the way you would normally think of it. Circulation is a mathematical concept used to explain the motion of air from a frame of reference bound to the wing. It is useful in understanding relative motion above and below the wing.
A similar situation might be a person walking toward the back of a train. The person can walk at 2mph and the train runs at 80mph, so is the person going forward or backward? The answer depends on your frame of reference: backward if you are on the train, forward if you standing by the tracks. Don't even ask about the direction from space.)
The simplest way to think of it is that airfow above the wing is moving faster than that below the wing, which gives the wing its lift. The cause is immaterial. For illustration assume a mach .8 aircraft has mach .88 airflow above its wing and mach .72 below. All molecules move to the trailing edge. If you want to compare these two flows, it is useful to subtract out the aircraft forward speed of .8 leaving mach +0.08 above the wing and -0.08 below, which defines the circulation. The negative speed (forward) below the wing only exists mathematically.

Interesting analogy with the train, but I am still not clear on this circulation concept.  Because from the relative position of an observer on the wing, the air molecules are still moving from the leading edge to the trailing edge.  Can you help me better understand what this means?

@MichaelHall The simplest way to think of it is that airfow above the wing is moving faster than that below the wing, which gives the wing its lift. The cause is immaterial. For illustration assume a mach .8 aircraft has mach .88 airflow above its wing and mach .72 below. All molecules move to the trailing edge as you suppose. If you want to compare these two flows, it is useful to subtract out the aircraft forward speed of .8 leaving mach +0.08 above the wing and -0.08 below, which defines the circulation. The negative speed (forward) below the wing only exists mathematically.

Got it, thanks!

Just because there's net circulation doesn't mean the fluid is rotating around the airfoil. That's not the definition is circulation.

@JZYL, "...doesn't mean the fluid is rotating around the airfoil." Yet that's exactly how it is depicted, hence the opportunity for confusion.  (there I was, flying along in the kutta condition, when suddenly...)

I very much like @Gerry's answer. It illustrates the principle of lift through potential theory very well.
I would like to add that circulation doesn't mean that fluid particles are rotating around the airfoil. In fact, even a simple rotating cylinder in an inviscid/irrotational flow would have well-defined streamlines flowing from upstream to downstream.
Rather, the integral definition of circulation in the OP is defined on a closed contour around the velocity vector field, not on a trajectory of any fluid particle. Intuitively, then, circulation illustrates how much a uniform flow has turned.
From Wolfram

My understanding so far: circulation is a mathematical circulation of a field of vectors around a contour (nothing physical). We can use a holomorphic transform of this to obtain this. Moving the rear stagnation point to the trailing point starts the downwash and creates a transient opposite actual / physical vortex behind, which then disappears (more). But that's no so clear, that's why no answer is yet selected.

@mins Do you have a reference on who said these two are holomorphic? The first one is a non-lifting cylinder. As explained by Gerry, the circulation around the cylinder is zero. The second one has a non-zero circulation if you enclose the airfoil with any closed curve. The stagnation points are not the cause for circulation. If you explain what is not clear, maybe we can adjust our answers.

I've found several mentions of conformal mapping (e.g. at Nasa), which according this (end of second page) is a holomorphic function.

@mins Yes, you can transform the circulation of an airfoil to that of a rotating cylinder. But the first image in your previous comment was a non-rotating cylinder. So there is no mapping between the two. Kutta condition dictates where the stagnation point should be on the airfoil, but itself does not give rise to lift. Circulation does.

Ok, I got this image from a page (unfortunately in French), where the cylinder wasn't rotating, but a holomorphic transform was yet mentioned.

@mins When we say holomorphic transformation, we are talking about a coordinate transformation. You can twist the cylinder into any airfoil shape, without any concept of fluid dynamics. Next, as mentioned in your second article, singularities (i.e. source, sink, vortex) in the original coordinates are still singularities in the twisted coordinates. The airfoil streamlines you refer to in the French article is that of doublets. I'll bet that when you calculate the circulation, it's zero. If you read further, it starts to talk about circulation and vortex flow.

@mins Can you please modify your OP to include any further confusion you have that has not been answered at the current state?

Many people seem to have not understood circulation. As shown in the figure, the circulation is shown as a blue curve with arrows, which is a curved motion and can be said to be a vortex. Of course, there is actually no clockwise flow around the wing as indicated by the pink arrow.
Because of the curved motion indicated by the blue arrow, or rather a vortex, there is lift from the wing.
Wing lift is like a high-speed roller coaster. A roller coaster moving along the outer track will reduce the pressure on the track (think about the pressure on the upper surface of the wing), while a roller coaster moving along the inner track will increase the pressure on the track (think about the pressure on the lower surface of the wing).

"the circulation is shown as a blue curve with arrows" that's not the circulation, that's the combination between the freestream and the circulation induced by the airfoil. "there is actually no clockwise flow around the wing" actually there is, see for example the second figure in this answer...

@sophit Assuming there are no wings, don't you think the flow shown by the blue curve is a circulation?

If there were no wing then air would just flow straight on

@sophit  As you said about actual flow, what I said is also in actual flow, there are no air molecules flowing around the wings.

"there are no air molecules flowing around the wings" yes there are. If you subtract the freestream then the air around an airfoil goes 1) up in front of it 2) backward on the upper surface 3) down on the back and 4) forward on the belly $\rightarrow$ that's just a very nice circle around the airfoil. Again, see the second picture in this answer.

@sophit What I'm talking about is actual flow, not subtracting freestream. Your method is only used to understand actual flow. Not the actual flow path of particles.


text:
Are transport gliders used by modern armies?
Famous WW2 operations involved transport gliders, for troops landing and vehicles transportation behind front lines. Gliders were cheap and quiet aircraft. The advantage over individual parachutes were landings grouped in a smaller area, allowing troops to be quickly operational.

XCG-16 assault glider, source: Retro-Mechanix
Browsing online seems to show an absence of gliders in the modern era. Are there any military (transport/troop) gliders in use in modern armies?

I believe HAHO and HALO jumps are the modern methods to insert troops silently behind enemy lines.

I don't think any modern transport airplane has such towing capabilities any more,

@kevin And the helicopter

Military gliders were often called "flying coffins" by troops, modern insertion methods really did away with their use after WW-II (and even near the end of the war).

Related: Joint Precision Air Drop System (JPADS)

@ymb1: Do you feel like writing an answer? Also the MMIST CQ-10.

No, there are no modern military glider forces, the Soviets kept an active glider force up until the early 60's before they retired them. All other military forces retired them before that because they really are not an effective delivery platform; they were inaccurate, often landing many miles off target, and had high rate of loss.
Gliders also tie up a large number of tow airplanes. Helicopters are much more capable, you can land troops on the tops of buildings or small clearings and are re-usable as well - gliders are generally non-recoverable as even if they are intact after landing they are often in inaccessible areas. Transport airplanes like C130s can land on very short, unprepared strips, or use the Low Altitude Parachute Extraction to deliver supplies without landing.

Not to forget that with parafoil chutes and GPS control all kinds of loads can be silently and precisely delivered. Helicopters and transport airplanes are too noisy and no real competition.

Although this is technically true, you are omitting a very important parameter: energy costs. Gliders, although less reliable, made economical sense in the context of WW2 when oil was much less plentiful than it is nowadays.
The example you give, the helicopter, would be much less interesting with higher fuel costs (those of WW2 or those of post peak oil or those due to a carbon tax for instance). A plane like the Osprey is actually much more interesting for troop delivery than the helicopter precisely because of its lower fuel needs.
With rising fuel prices, gliders could get an edge again.

Glider assault landings during the Second World War proved inherently hazardous, more so than parachute drops, and crashes typically resulted in deaths and serious injuries among the personnel being transported even in the absence of enemy opposition, while the gliders themselves were often destroyed or damaged beyond repair. In addition to transporting troops, gliders were used to deliver heavy equipment, up to small tanks. The development in the 1950s of large turboprop engined transport aircraft such as the Lockheed C130 Hercules, with facilities for short field operation, rapid loading and unloading and the para dropping of large items of equipment largely eliminated any further need for military gliders, although special forces today are sometimes trained in the use of para gliders for infiltration.

This was before radars, on board computers, GPS, satellite weather and wind tracking though, moreover, most of those flights took place at night to avoid detection. Reliability nowadays would be much higher even in much worse weather conditions.